OCN 5401 Chapter 5 Equations of Motion Instructor: Dr. George A. Maul / X 7453.

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Presentation transcript:

OCN 5401 Chapter 5 Equations of Motion Instructor: Dr. George A. Maul / X 7453

Forces affecting seawater (excluding tidal forces, etc.) Acceleration = Pressure gradient force + Coriolis force + Gravity + Friction Infrared Image of Florida Current

Foucault Pendulum Jean Bernard Léon Foucault t in seconds; n o in degrees per sidereal day Ultimate proof (1851) that Earth rotates! BUT Aristarchus BC thought so too!

Gravitation and Gravity Toward Earth’s center (d Earth ≈6378 km) Earth’s rotation Ω causes two apparent forces: gravity and Coriolis outward

Coriolis Effect watch?v=mcPs_OdQOYU Gaspard-Gustave de Coriolis

Coriolis Parameter (f) Earth rotates 2π radians in 23 h 56 m 4.1 s one sidereal day. On a rotating planet, centrifugal force is Ω 2 R, where R is the radius at that latitude. Now if a parcel moves eastward at speed U, there is an added angular velocity U/R. The new total force: 0.729x10 -4 Coriolis force

Ocean Currents are nearly geostrophic: Coriolis balances Pressure Gradient

Horizontal Pressure Gradient Force (per unit mass) level surface (geoid) sea surface p2p2 p1p1 ΔxΔx h2h2 h1h1 Units?

Role of Surface Friction Fill lows and empty highs

Austausch Coefficients also called exchange coefficient, eddy coefficient, or eddy diffusivity Compare with dynamic (molecular) viscosity for laminar flow: and A z is probably depth dependent

Vertical Friction

Horizontal Friction Gulf Stream cross-current model velocity shear friction

Global Sea Surface Dynamic Topography Not the Geoid!

Sea Surface Dynamic Topography Variability

Oceanic Eddies Vorticity

Relative Vorticity (ζ)

Beta plane (beta a constant – usually over mid-latitudes)

Absolute Vorticity (ζ A ) and Divergence (D h )

Charleston Bump Retroflection Gulf Stream Meanders Potential Vorticity Conservation

Approximations

OCN 5401 Questions? Chapter 5